Generalization from tripartite to multipartite separability

Determine whether the holographic dual of relative entropy with respect to the set of $m$-partite separable states is governed, at leading order, by a minimal $m$-partition surface in the bulk, and whether the arguments established for tripartite separability extend to this setting.

Background

The paper proposes a bulk minimal tripartition surface as the geometric dual of the relative entropy of entanglement for a boundary tripartition. This raises the possibility that analogous geometric objects control relative entropies defined with respect to more general multipartite-separable state sets.

The authors explicitly formulate this extension as a conjecture and ask whether their tripartite arguments can be generalized to arbitrary numbers of parties.